This table of 167edo intervals assumes 13-limit patent val ⟨167 265 388 469 578 618].
Intervals highlighted in bold are prime harmonics or subharmonics. Intervals that differ from their assigned steps by more than 50%, but no more than 100%, are shown in italic. Intervals that differ by more than 100% or with odd limit over 800 are not shown. For clarity, an entry can contain multiple intervals if they are of comparable complexity.
| #
|
Cents
|
Marks
|
5-limit
|
7-limit
|
11-limit
|
13-limit
|
| 0
|
0.00
|
P1
|
1/1
|
| 1
|
7.186
|
|
|
126/125, 225/224
|
121/120, 176/175, 243/242
|
144/143, 169/168, 196/195
|
| 2
|
14.371
|
|
81/80
|
|
99/98, 100/99, 121/120
|
91/90, 105/104
|
| 3
|
21.557
|
|
81/80
|
64/63
|
|
65/64, 66/65, 78/77
|
| 4
|
28.743
|
|
|
49/48, 50/49, 64/63, 686/675
|
55/54, 56/55
|
648/637
|
| 5
|
35.928
|
|
|
49/48
|
45/44
|
|
| 6
|
43.114
|
|
|
36/35, 525/512
|
|
40/39, 693/676
|
| 7
|
50.299
|
|
250/243
|
36/35
|
33/32, 605/588
|
|
| 8
|
57.485
|
|
|
28/27
|
33/32
|
65/63, 91/88, 336/325
|
| 9
|
64.671
|
|
25/24
|
|
|
26/25, 27/26
|
| 10
|
71.856
|
|
25/24
|
|
704/675
|
715/686
|
| 11
|
79.042
|
|
|
21/20
|
22/21
|
245/234
|
| 12
|
86.228
|
|
|
21/20
|
81/77
|
104/99
|
| 13
|
93.413
|
m2
|
|
|
|
55/52, 96/91, 325/308, 343/325
|
| 14
|
100.599
|
|
|
|
35/33
|
143/135, 441/416, 675/637
|
| 15
|
107.784
|
|
16/15
|
|
|
117/110, 484/455, 715/672
|
| 16
|
114.970
|
|
16/15
|
15/14
|
77/72, 576/539
|
125/117
|
| 17
|
122.156
|
|
|
15/14
|
189/176
|
14/13, 130/121, 338/315
|
| 18
|
129.341
|
|
|
|
264/245
|
14/13
|
| 19
|
136.527
|
|
|
|
250/231
|
13/12, 225/208
|
| 20
|
143.713
|
|
|
49/45
|
12/11, 88/81
|
13/12
|
| 21
|
150.898
|
|
|
|
12/11
|
|
| 22
|
158.084
|
|
|
35/32, 192/175
|
11/10, 675/616
|
128/117, 325/297, 351/320, 385/351, 429/392
|
| 23
|
165.269
|
|
|
|
11/10
|
845/768
|
| 24
|
172.455
|
|
|
54/49
|
243/220, 495/448, 875/792
|
182/165
|
| 25
|
179.641
|
|
10/9
|
|
256/231
|
72/65, 195/176, 231/208, 375/338, 416/375
|
| 26
|
186.826
|
|
10/9
|
|
49/44, 891/800
|
39/35
|
| 27
|
194.012
|
|
|
28/25
|
|
143/128, 160/143, 189/169
|
| 28
|
201.198
|
M2
|
9/8
|
|
55/49
|
91/81, 702/625
|
| 29
|
208.383
|
|
9/8
|
|
|
44/39, 273/242
|
| 30
|
215.569
|
|
|
|
25/22, 112/99
|
162/143
|
| 31
|
222.754
|
|
|
|
25/22
|
91/80
|
| 32
|
229.940
|
|
|
8/7
|
|
297/260, 490/429
|
| 33
|
237.126
|
|
|
8/7
|
55/48
|
416/363, 650/567
|
| 34
|
244.311
|
|
144/125
|
|
121/105
|
15/13, 539/468
|
| 35
|
251.497
|
|
|
81/70
|
140/121
|
15/13, 52/45
|
| 36
|
258.683
|
|
|
512/441
|
64/55
|
65/56
|
| 37
|
265.868
|
|
|
7/6, 400/343
|
|
|
| 38
|
273.054
|
|
75/64
|
7/6
|
|
117/100
|
| 39
|
280.240
|
|
|
147/125, 288/245
|
33/28, 88/75
|
|
| 40
|
287.425
|
|
|
189/160, 405/343
|
|
13/11
|
| 41
|
294.611
|
m3
|
32/27
|
|
|
13/11
|
| 42
|
301.796
|
|
|
25/21
|
|
|
| 43
|
308.982
|
|
6/5
|
448/375
|
105/88, 484/405
|
117/98, 140/117
|
| 44
|
316.168
|
|
6/5
|
|
605/504
|
|
| 45
|
323.353
|
|
|
135/112
|
|
65/54
|
| 46
|
330.539
|
|
|
98/81
|
40/33, 121/100
|
63/52
|
| 47
|
337.725
|
|
|
175/144
|
40/33, 147/121
|
39/32, 91/75
|
| 48
|
344.910
|
|
625/512
|
128/105
|
11/9, 336/275
|
39/32, 825/676
|
| 49
|
352.096
|
|
|
49/40
|
11/9, 27/22
|
364/297
|
| 50
|
359.281
|
|
|
|
|
16/13
|
| 51
|
366.467
|
|
100/81
|
|
99/80, 121/98
|
16/13, 26/21, 225/182
|
| 52
|
373.653
|
|
|
|
150/121
|
26/21, 242/195, 273/220
|
| 53
|
380.838
|
|
5/4
|
56/45
|
|
81/65
|
| 54
|
388.024
|
|
5/4
|
|
|
169/135, 429/343, 1001/800
|
| 55
|
395.210
|
|
|
|
44/35
|
49/39
|
| 56
|
402.395
|
|
|
63/50
|
44/35, 121/96, 125/99, 486/385
|
525/416
|
| 57
|
409.581
|
M3
|
81/64
|
|
308/243, 792/625
|
33/26, 195/154
|
| 58
|
416.766
|
|
|
|
14/11
|
|
| 59
|
423.952
|
|
32/25
|
125/98
|
14/11
|
143/112, 216/169
|
| 60
|
431.138
|
|
32/25
|
9/7
|
77/60, 440/343
|
50/39
|
| 61
|
438.323
|
|
|
9/7
|
165/128, 567/440
|
156/121, 676/525
|
| 62
|
445.509
|
|
|
35/27
|
128/99
|
84/65, 507/392
|
| 63
|
452.695
|
|
|
|
100/77, 891/686
|
13/10
|
| 64
|
459.880
|
|
|
64/49
|
176/135
|
13/10, 441/338, 845/648
|
| 65
|
467.066
|
|
|
21/16
|
55/42
|
|
| 66
|
474.251
|
|
|
21/16
|
405/308
|
130/99, 154/117
|
| 67
|
481.437
|
|
|
|
33/25
|
169/128, 416/315
|
| 68
|
488.623
|
|
|
|
175/132, 297/224
|
65/49
|
| 69
|
495.808
|
P4
|
4/3
|
|
|
225/169
|
| 70
|
502.994
|
|
4/3
|
75/56
|
147/110
|
234/175
|
| 71
|
510.180
|
|
|
75/56, 168/125
|
121/90
|
35/26, 192/143
|
| 72
|
517.365
|
|
27/20
|
|
66/49
|
182/135
|
| 73
|
524.551
|
|
27/20
|
|
|
65/48, 88/65
|
| 74
|
531.737
|
|
|
49/36, 200/147
|
15/11, 110/81
|
495/364, 972/715
|
| 75
|
538.922
|
|
512/375
|
|
15/11
|
273/200
|
| 76
|
546.108
|
|
|
48/35
|
11/8
|
196/143, 351/256, 891/650
|
| 77
|
553.293
|
|
|
135/98
|
11/8, 500/363
|
260/189
|
| 78
|
560.479
|
|
864/625
|
112/81
|
|
18/13, 539/390
|
| 79
|
567.665
|
|
25/18
|
|
168/121
|
18/13
|
| 80
|
574.850
|
|
25/18
|
1024/735
|
675/484
|
39/28
|
| 81
|
582.036
|
|
|
7/5, 480/343
|
|
|
| 82
|
589.222
|
d5
|
45/32, 1024/729
|
7/5
|
|
|
| 83
|
596.407
|
|
45/32
|
343/243, 882/625
|
484/343
|
55/39
|
| 84
|
603.593
|
|
64/45
|
625/441
|
343/242
|
78/55
|
| 85
|
610.778
|
A4
|
64/45, 729/512
|
10/7
|
|
845/594
|
| 86
|
617.964
|
|
|
10/7, 343/240
|
|
|
| 87
|
625.150
|
|
36/25
|
735/512, 1125/784
|
|
56/39
|
| 88
|
632.335
|
|
36/25
|
|
121/84
|
13/9
|
| 89
|
639.521
|
|
625/432
|
81/56
|
|
13/9
|
| 90
|
646.707
|
|
|
|
16/11, 363/250
|
189/130
|
| 91
|
653.892
|
|
|
35/24
|
16/11
|
143/98, 512/351
|
| 92
|
661.078
|
|
375/256
|
|
22/15
|
343/234
|
| 93
|
668.263
|
|
|
[72/49]], 147/100
|
22/15, 81/55
|
715/486
|
| 94
|
675.449
|
|
40/27
|
|
|
65/44
|
| 95
|
682.635
|
|
40/27
|
|
49/33
|
135/91
|
| 96
|
689.820
|
|
|
112/75, 125/84
|
49/33
|
52/35, 143/96
|
| 97
|
697.006
|
|
3/2
|
112/75
|
121/81
|
175/117
|
| 98
|
704.192
|
P5
|
3/2
|
|
|
338/225
|
| 99
|
711.377
|
|
|
|
264/175, 448/297
|
98/65
|
| 100
|
718.563
|
|
|
50/33
|
256/169, 315/208
|
| 101
|
725.749
|
|
|
32/21
|
616/405
|
99/65, 117/77
|
| 102
|
732.934
|
|
|
32/21
|
55/36, 84/55
|
|
| 103
|
740.120
|
|
|
49/32
|
135/88
|
20/13, 676/441
|
| 104
|
747.305
|
|
|
|
77/50
|
20/13
|
| 105
|
754.491
|
|
|
54/35
|
99/64
|
65/42, 784/507
|
| 106
|
761.677
|
|
|
14/9
|
256/165
|
121/78, 525/338
|
| 107
|
768.862
|
|
25/16
|
14/9
|
120/77, 343/220
|
39/25
|
| 108
|
776.048
|
|
25/16
|
|
11/7
|
169/108
|
| 109
|
783.234
|
|
|
|
11/7
|
|
| 110
|
790.419
|
m6
|
128/81
|
|
243/154, 625/396
|
52/33
|
| 111
|
797.605
|
|
|
100/63
|
35/22, 198/125, 385/243
|
165/104, 507/320, 832/525
|
| 112
|
804.790
|
|
|
|
35/22
|
78/49
|
| 113
|
811.976
|
|
8/5
|
|
1125/704
|
270/169, 686/429
|
| 114
|
819.162
|
|
8/5
|
45/28
|
77/48
|
130/81
|
| 115
|
826.347
|
|
|
|
121/75
|
21/13, 195/121, 440/273
|
| 116
|
833.533
|
|
81/50
|
|
196/121
|
13/8, 21/13, 364/225
|
| 117
|
840.719
|
|
|
|
|
13/8
|
| 118
|
847.904
|
|
|
49/30, 80/49
|
18/11, 44/27
|
297/182
|
| 119
|
855.090
|
|
1024/625
|
105/64
|
18/11, 275/168
|
64/39, 819/500
|
| 120
|
862.275
|
|
|
288/175
|
33/20, 242/147
|
150/91
|
| 121
|
869.461
|
|
|
81/49
|
33/20, 200/121
|
945/572
|
| 122
|
876.647
|
|
|
81/49, 224/135
|
|
91/55, 108/65
|
| 123
|
883.832
|
|
5/3
|
|
1008/605
|
693/416
|
| 124
|
891.018
|
|
5/3
|
375/224
|
405/242
|
117/70
|
| 125
|
898.204
|
|
|
42/25
|
|
|
| 126
|
905.389
|
M6
|
27/16
|
|
1225/726
|
22/13
|
| 127
|
912.575
|
|
|
320/189, 686/405
|
847/500
|
22/13
|
| 128
|
919.760
|
|
|
245/144
|
56/33, 75/44, 1029/605
|
143/84
|
| 129
|
926.946
|
|
128/75
|
12/7, 875/512
|
75/44, 77/45
|
169/99, 1155/676
|
| 130
|
934.132
|
|
|
12/7, 343/200
|
|
|
| 131
|
941.317
|
|
|
441/256
|
55/32
|
112/65
|
| 132
|
948.503
|
|
|
|
121/70
|
26/15, 45/26
|
| 133
|
955.689
|
|
125/72
|
|
|
26/15, 936/539
|
| 134
|
962.874
|
|
|
7/4
|
96/55
|
363/208, 567/325
|
| 135
|
970.060
|
|
|
7/4
|
|
429/245
|
| 136
|
977.246
|
|
|
|
44/25
|
160/91
|
| 137
|
984.431
|
|
|
|
44/25, 99/56
|
39/22, 143/81, 1125/637
|
| 138
|
991.617
|
|
16/9
|
|
|
39/22, 484/273
|
| 139
|
998.802
|
m7
|
16/9
|
|
98/55
|
162/91, 625/351
|
| 140
|
1005.988
|
|
|
25/14
|
|
143/80, 338/189
|
| 141
|
1013.174
|
|
9/5
|
|
88/49
|
70/39
|
| 142
|
1020.359
|
|
9/5
|
|
231/128
|
65/36, 375/208
|
| 143
|
1027.545
|
|
|
49/27, 405/224
|
440/243, 896/495
|
165/91
|
| 144
|
1034.731
|
|
|
|
20/11
|
|
| 145
|
1041.916
|
|
|
64/35, 175/96
|
20/11, 1125/616
|
117/64, 594/325, 640/351, 702/385, 715/392, 1183/648
|
| 146
|
1049.102
|
|
|
|
11/6
|
|
| 147
|
1056.287
|
|
|
|
11/6, 81/44
|
24/13
|
| 148
|
1063.473
|
|
|
|
231/125
|
24/13, 1183/640
|
| 149
|
1070.659
|
|
|
|
245/132
|
13/7
|
| 150
|
1077.844
|
|
|
28/15
|
|
13/7, 121/65, 315/169
|
| 151
|
1085.030
|
|
15/8
|
|
144/77, 539/288
|
234/125
|
| 152
|
1092.216
|
|
15/8
|
|
1323/704
|
169/90, 220/117, 455/242
|
| 153
|
1099.401
|
|
|
|
66/35
|
49/26, 270/143, 832/441, 1274/675
|
| 154
|
1106.587
|
M7
|
|
|
|
91/48, 616/325, 650/343
|
| 155
|
1113.772
|
|
|
40/21
|
21/11
|
99/52
|
| 156
|
1120.958
|
|
|
|
21/11, 275/144
|
468/245
|
| 157
|
1128.144
|
|
48/25
|
|
675/352
|
25/13, 1372/715
|
| 158
|
1135.329
|
|
|
27/14
|
|
25/13, 52/27
|
| 159
|
1142.515
|
|
|
27/14
|
64/33
|
126/65, 176/91, 325/168
|
| 160
|
1149.701
|
|
243/125
|
35/18
|
1176/605
|
|
| 161
|
1156.886
|
|
|
35/18, 1024/525
|
|
39/20, 1352/693
|
| 162
|
1164.072
|
|
|
49/25, 96/49
|
|
1375/702
|
| 163
|
1171.257
|
|
|
49/25, 63/32, 675/343
|
55/28
|
637/324, 1125/572
|
| 164
|
1178.443
|
|
160/81
|
63/32
|
|
65/33, 77/39
|
| 165
|
1185.629
|
|
|
125/63
|
99/50, 240/121
|
|
| 166
|
1192.814
|
|
|
125/63, 448/225
|
175/88, 484/243
|
143/72, 195/98
|
| 167
|
1200.000
|
P8
|
2/1
|